Details

sample76.0ms

Algorithm

intervals

Results

55.0ms

621×

body

valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	4021
3	726
2	183
1	56
0	18

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)
0.1b	(* (* a a) (- 1 a))
0.3b	(pow (+ (* a a) (* b b)) 2)
0.6b	(* (* b b) (+ 3 a))

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
27×	`prod-diff` `add-cube-cbrt`
16×	`add-exp-log`
15×	`pow1`
14×	`add-cbrt-cube`
12×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-r`
9×	`add-log-exp`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow` `sub-neg` `unpow-prod-down` `fma-neg`
2×	`flip3--` `diff-log` `associate-l` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`pow-to-exp` `expm1-def` `sum-log` `pow-pow` `flip3-+` `difference-of-sqr-1` `pow-exp` `associate--l+` `flip-+` `distribute-lft-out` `unpow2` `sqr-pow`

Counts

4 → 131

Calls

4 calls:

471.0ms	(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)
53.0ms	(* (* a a) (- 1 a))
16.0ms	(pow (+ (* a a) (* b b)) 2)
23.0ms	(* (* b b) (+ 3 a))

series328.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)
92.0ms	(* (* a a) (- 1 a))
45.0ms	(pow (+ (* a a) (* b b)) 2)
47.0ms	(* (* b b) (+ 3 a))

simplify2.3s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2506
1	768
0	256

prune651.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (+ 3 a))
0.6b	(* (* b b) (+ 3 a))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-r` `add-cube-cbrt`
6×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `associate-*r/` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

34.0ms	(* (* b b) (+ 3 a))
27.0ms	(* (* b b) (+ 3 a))
59.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
53.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

series972.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* b b) (+ 3 a))
55.0ms	(* (* b b) (+ 3 a))
640.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
230.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5006
2	1485
1	347
0	118

prune777.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4 (- (* a a) (* a (* a a))) (fma (fma a 4 12) (* b b) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
0.0b	(- (* a a) (* a (* a a)))
0.1b	(* a (* a a))
0.2b	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity` `pow-prod-up` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`fma-udef`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `fma-neg` `diff-log` `cube-unmult` `associate-r` `prod-diff` `pow-sqr` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

0.0ms	(fma 4 (- (* a a) (* a (* a a))) (fma (fma a 4 12) (* b b) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
9.0ms	(- (* a a) (* a (* a a)))
14.0ms	(* a (* a a))
0.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

series455.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(fma 4 (- (* a a) (* a (* a a))) (fma (fma a 4 12) (* b b) (fma (fma a a (* b b)) (fma a a (* b b)) -1)))
98.0ms	(- (* a a) (* a (* a a)))
67.0ms	(* a (* a a))
124.0ms	(fma (fma a a (* b b)) (fma a a (* b b)) -1)

simplify1.9s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	2657
2	630
1	238
0	110

prune421.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (+ 3 a))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `pow1`
10×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
8×	`add-cube-cbrt`
6×	`sqrt-div`
4×	`expm1-log1p-u` `flip3-+` `associate-r` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative` `distribute-lft-out` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

23.0ms	(* (* b b) (+ 3 a))
61.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
48.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
61.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* b b) (+ 3 a))
190.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
207.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
218.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

simplify1.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5006
2	1485
1	347
0	118

prune676.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes363.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	14

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.6s

20480×

body

valid